What you call "server side rendering" is a new buzzword for simple classic "HTTP response". How you structure you app and how you load your templates is noway connected to HTTP cookies.
Usually server in HTTP response sends Set-Cookie header telling browser to create a new cookie.
Sometimes it is needed to create a cookie from a browser and it is done by a document.cookie
Browser sends all cookies itself on each HTTP request.
More information about HTTP Cookies on MDN